Global maximum of ?(x)-x

[Gerald McGarvey]

Another question is: Where does []x - x have a global maximum?,
where []x is the Conway box function (the inverse of Minkowski's
question mark function). Some info on []x is at
http://en.wikipedia.org/wiki/Minkowski_question_mark_function
(which answers my question about ?(1-x)+?(x)). I'm working on PARI
code for []x.

- Gerry

At 09:02 AM 6/12/2006, Antti Karttunen wrote:
>Antti Karttunen wrote:
>
>>Gene Smith wrote:
>>
>>>
>>>
>>>On 6/10/06, *Joseph Biberstine* <jrbibers at indiana.edu 
>>><mailto:jrbibers at indiana.edu>> wrote:
>>>
>>>             Not clever enough to figure this out a reliable
>>>     computation of this
>>>     myself.  Please help find enough accurate terms for OEIS and I will of
>>>     course credit you.
>>>
>>>             Consider f(x) := ?(x)-x where ?(x) is Minkowski's question
>>>     mark function.
>>>             Recently I've wondered at what value xmax f will obtain
>>>     its global
>>>     maximum (mod 1).
>>>
>>>Another question is where does ?(x)=x, aside from the obvious places at 
>>>integers and half integers.
>>
>>
>>http://www.research.att.com/~njas/sequences/?q=fixed+Minkowski&sort=0&fmt=0&language=english&go=Search 
>>
>>(Of course there is a second non-trivial fixed point at 1- 0.42037... if 
>>I recall right.)
>Yes, it's confrac has been already submitted by Joseph as:
>http://www.research.att.com/~njas/sequences/A120221
>
>-- Antti.